Brian is filling a basket with bananas of equal weight. Draw a graph and write an equation to represent this situation.
The table shows the relationship between the number of bananas and the total weight of the basket. After 2 bananas, the total weight of the basket is 32 ounces. After 6 bananas, the total weight is 72 ounces. Plot the two points on the graph to show the total weight of the basket of bananas after 2 bananas and 6 bananas are put in the basket.
Number of bananas Total weight (oz)
2 32
6 72
You got it!
For each banana added to the basket, the total weight increases at a constant rate. So, we can draw a line through these two points to show the linear relationship between the number of bananas and the total weight in ounces. Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line?
x
y
(2, 32)(6, 72)
0
1
2
3
4
5
6
7
8
9
10
0
8
16
24
32
40
48
56
64
72
80
88
96
104
Number of bananas
Total weight (oz)
y= mx + b
Slope =
\(m = \frac{72-32}{6-2} = \frac{40}{4} = 10\)
Since the slope represents the increase in total weight for each additional banana, the slope of 10 means that each banana adds 10 ounces to the total weight of the basket.
Now, we can use one of the points to find the y-intercept (b) in the equation y = mx + b. Let's use the point (2, 32):
\(32 = 10(2) + b\)
\(32 = 20 + b\)
\(b = 12\)
Therefore, the equation that represents the relationship between the number of bananas and the total weight of the basket is:
\(y = 10x + 12\)
You can plot the points (2, 32) and (6, 72) on a graph and draw a line that represents this linear relationship.